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US8113667B2 - Projection optical system - Google Patents

Projection optical system Download PDF

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Publication number
US8113667B2
US8113667B2 US12/529,242 US52924208A US8113667B2 US 8113667 B2 US8113667 B2 US 8113667B2 US 52924208 A US52924208 A US 52924208A US 8113667 B2 US8113667 B2 US 8113667B2
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Prior art keywords
screen
projection
screen surface
distance
absolute value
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US12/529,242
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US20100118281A1 (en
Inventor
Keiko Yamada
Kohtaro Hayashi
Soh Ohzawa
Masayuki Imaoka
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Konica Minolta Opto Inc
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Konica Minolta Opto Inc
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Assigned to KONICA MINOLTA OPTO, INC. reassignment KONICA MINOLTA OPTO, INC. ASSIGNMENT OF ASSIGNORS INTEREST (SEE DOCUMENT FOR DETAILS). Assignors: OHZAWA, SOH, HAYASHI, KOHTARO, IMAOKA, MASAYUKI, YAMADA, KEIKO
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    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B17/00—Systems with reflecting surfaces, with or without refracting elements
    • G02B17/08—Catadioptric systems
    • G02B17/0804—Catadioptric systems using two curved mirrors
    • G02B17/0816—Catadioptric systems using two curved mirrors off-axis or unobscured systems in which not all of the mirrors share a common axis of rotational symmetry, e.g. at least one of the mirrors is warped, tilted or decentered with respect to the other elements
    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03B—APPARATUS OR ARRANGEMENTS FOR TAKING PHOTOGRAPHS OR FOR PROJECTING OR VIEWING THEM; APPARATUS OR ARRANGEMENTS EMPLOYING ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ACCESSORIES THEREFOR
    • G03B21/00—Projectors or projection-type viewers; Accessories therefor
    • G03B21/005—Projectors using an electronic spatial light modulator but not peculiar thereto
    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03B—APPARATUS OR ARRANGEMENTS FOR TAKING PHOTOGRAPHS OR FOR PROJECTING OR VIEWING THEM; APPARATUS OR ARRANGEMENTS EMPLOYING ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ACCESSORIES THEREFOR
    • G03B21/00—Projectors or projection-type viewers; Accessories therefor
    • G03B21/14—Details
    • G03B21/28—Reflectors in projection beam

Definitions

  • the present invention relates to a projection optical system and relates to, for example, a projection optical system that is incorporated in an image projection apparatus having a display device such as a liquid crystal display device or a digital micromirror device and that enlarges and projects an image on a display device surface onto a screen surface.
  • the invention also relates to a projection optical instrument (in particular, a projection image display apparatus) incorporating such a projection optical system.
  • One known way to reduce a projection space required outside a projector to provide a larger screen is to introduce a reflective surface into a projection optical system to fold, into the projection optical system, an optical path of a light beam used for forming a projected image.
  • Another known way is to increase the angle of incidence of a light beam with respect to a screen surface to reduce the distance from a projection optical system to a screen.
  • patent document 1 there is proposed a construction in which an optical path is folded by a reflective surface and this increases the angle of incidence of a light beam to reduce a projection space.
  • Patent document 1 JP-A-2004-258620
  • Patent document 2 JP-A-2006-184775
  • Patent document 3 JP-A-2005-106900
  • an optical path within a projection optical system is folded by a reflective surface, and the angle of incidence of rays with respect to a screen surface is increased, with the result that the screen of a projector can be increased in size and a projection space can be reduced.
  • the difference between the length of the optical path of rays incident on the screen upper ends of the screen surface and the length of the optical path of rays incident on the screen lower ends of the screen surface is increased. Consequently, when a projection distance is varied, trapezoidal distortion is significantly produced, and it is thus necessary to correct the trapezoidal distortion simultaneously when focus is adjusted.
  • patent document 1 Since a construction that can achieve focus is not disclosed in patent document 1, it is difficult to provide, with its projection optical system, a construction that can achieve focus.
  • patent documents 2 and 3 there is specifically proposed no method for correcting trapezoidal distortion that is produced when the angle of incidence of rays with respect to a screen is increased and simultaneously a projection distance is varied.
  • the use of projection optical systems proposed in patent document 2 and 3 makes it difficult to correct trapezoidal distortion and obtain satisfactory performance.
  • a projection optical system that receives light from a display device surface and enlarges and projects a display image thereon obliquely onto a screen surface and that varies a projection distance to a screen to display images of different projection magnifications, the projection optical system including one or more reflective surfaces having an optical power between the display device surface and the screen surface.
  • focus is adjusted by moving at least one optical device having an optical power, and conditional formula (1) below is satisfied: 0.01 ⁇ (tan ⁇ f 1 ⁇ tan ⁇ f 2) ⁇ (tan ⁇ n 1 ⁇ tan ⁇ n 2) ⁇ ( ⁇ 2/ ⁇ 1) ⁇ 0.20 (1)
  • the direction of a normal to the screen of the screen surface is referred to as a “z-direction”
  • the direction of a long side of the screen of the screen surface is referred to as an “x-direction”
  • the x-z plane component of the angle of incidence with respect to the screen surface is referred to as an “incident angle ⁇ (°)” and among rays that pass through the center of an aperture and that are incident on the ends of the upper and lower sides of the screen of the screen surface, the incident angle ⁇ of rays whose incident angle ⁇ is larger is referred to as “ ⁇ f” and the incident angle ⁇ of rays whose incident angle ⁇ is smaller is referred to as “ ⁇ n”,
  • a projection optical system that receives light from a display device surface and enlarges and projects a display image thereon obliquely onto a screen surface and that varies a projection distance to a screen to display images of different projection magnifications, the projection optical system including one or more reflective surfaces having an optical power between the display device surface and the screen surface.
  • focus is adjusted by moving at least one optical device having an optical power, and conditional formula (1) below is satisfied within at least a range specified by a formula “1.3 ⁇ 1/ ⁇ 2 ⁇ 1.8”: 0.01 ⁇ (tan ⁇ f 1 ⁇ tan ⁇ f 2) ⁇ (tan ⁇ n 1 ⁇ tan ⁇ n 2) ⁇ ( ⁇ 2/ ⁇ 1) ⁇ 0.20 (1)
  • the direction of a normal to the screen of the screen surface is referred to as a “z-direction”
  • the direction of a long side of the screen of the screen surface is referred to as an “x-direction”
  • the x-z plane component of the angle of incidence with respect to the screen surface is referred to as an “incident angle ⁇ (°)” and among rays that pass through the center of an aperture and that are incident on the ends of the upper and lower sides of the screen of the screen surface, the incident angle ⁇ of rays whose incident angle ⁇ is larger is referred to as “ ⁇ f” and the incident angle ⁇ of rays whose incident angle ⁇ is smaller is referred to as “ ⁇ n”,
  • a projection optical system that embodies the first or second aspect of the invention and that satisfies conditional formula (2): 38 ⁇ f ⁇ 80 (2)
  • a projection optical system that embodies the third aspect of the invention and in which a distance from the exit pupil of rays incident on the screen at the incident angle ⁇ f to the screen is shorter than a distance from the exit pupil of rays incident on the screen at the incident angle ⁇ n to the screen.
  • a projection optical system that embodies any one of the first to four aspects of the invention and that satisfies conditional formula (3): 1 ⁇ ( ⁇ 1+ ⁇ 2)/(2 ⁇ P 1) ⁇
  • a ray passing through the center of the aperture is referred to as a “pupil center ray”
  • the length of a normal falling perpendicularly on the screen surface from an intersection between a reflective surface that is located closest to the screen among the reflective surfaces having an optical power and the pupil center ray is the projection distance
  • a projection optical system that embodies any one of the first to fifth aspects of the invention and that satisfies conditional formula (4): 160 ⁇ ( x 1 /P 1) ⁇
  • a ray passing through the center of an aperture is referred to as a “pupil center ray”
  • the length of a normal falling perpendicularly on the screen surface from an intersection between a reflective surface that is located closest to the screen among the reflective surfaces having an optical power and the pupil center ray is the projection distance
  • a projection optical system that embodies any one of the first to sixth aspects of the invention and that satisfies conditional formula (5): ⁇ 0.02 ⁇ ( ⁇ 1 ⁇ 2) ⁇ 2 ⁇ / ⁇ ( ⁇ 1+ ⁇ 2) ⁇ 1 ⁇ 0.2 (5)
  • a projection optical system that embodies any one of the first to seventh aspects of the invention and that includes at least one refractive optical device having an optical power.
  • a projection optical system that embodies any one of the first to eighth aspects of the invention and in which the rotationally symmetrical axes of at least two optical devices coincide.
  • a projection optical system that embodies any one of the first to ninth aspects of the invention and in which at least one reflective surface is moved in the focus adjustment.
  • a projection optical system that embodies any one of the first to tenth aspects of the invention and in which at least one refractive optical device is moved in the focus adjustment.
  • a projection image display apparatus that includes a display device forming a two-dimensional image and a projection optical system enlarging and projecting an image on a display device surface thereof onto a screen surface, the projection optical system being the projection optical system that embodies any one of the first to eleventh aspects of the invention.
  • one or more reflective surfaces having an optical power are included and this makes it possible not only to increase the size of a screen but also to decrease a projection distance, and a focus mechanism is incorporated and this makes it possible to obtain a satisfactory projected image at an appropriate projection distance.
  • Focus performed under predetermined conditions allows trapezoidal distortion produced when a projection distance is varied to be satisfactorily corrected.
  • a projection optical system that maintains high optical performance, has a significantly decreased projection distance and achieves focus according to a distance to a screen and a projection display apparatus incorporating such a projection optical system.
  • FIG. 1 A ray diagram showing the optical construction of a first embodiment (Example 1);
  • FIG. 2 Spot diagrams of Example 1
  • FIG. 3 Distortion diagrams of Example 1
  • FIG. 4 A ray diagram showing the optical construction of a second embodiment (Example 2);
  • FIG. 5 Spot diagrams of Example 2.
  • FIG. 6 Distortion diagrams of Example 2.
  • FIG. 7 A ray diagram showing the optical construction of a third embodiment (Example 3);
  • FIG. 8 Spot diagrams of Example 3.
  • FIG. 9 Distortion diagrams of Example 3.
  • FIG. 10 A ray diagram showing the optical construction of a fourth embodiment (Example 4);
  • FIG. 11 Spot diagrams of Example 4.
  • FIG. 12 Distortion diagrams of Example 4.
  • FIG. 13 A ray diagram showing the optical construction of a fifth embodiment (Example 5);
  • FIG. 14 Spot diagrams of Example 5.
  • FIG. 15 Distortion diagrams of Example 5.
  • FIG. 16 A ray diagram showing the optical construction of a sixth embodiment (Example 6);
  • FIG. 17 Spot diagrams of Example 6
  • FIG. 18 Distortion diagrams of Example 6
  • FIG. 19 Schematic diagrams showing the difference between the position of the exit pupil of rays incident on the screen upper ends of a screen surface and the position of the exit pupil of rays incident on the screen lower ends of the screen surface;
  • FIG. 20 A schematic diagram showing a projection distance
  • FIG. 21 Schematic diagrams showing trapezoidal distortion produced when the projection distance is varied
  • FIG. 22 Schematic diagrams showing how trapezoidal distortion is corrected by varying an angle of incidence
  • FIG. 23 Schematic diagrams showing how trapezoidal distortion is corrected by moving an exit pupil.
  • the projection optical system of the invention receives light from a display device surface and enlarges and projects a display image thereon obliquely onto a screen surface, and varies a projection distance to a screen to display images of different projection magnifications.
  • the projection optical system includes one or more reflective surfaces having an optical power between the display device surface and the screen surface, and moves at least one optical device having an optical power to adjust focus.
  • the difference between the length of the optical path of rays incident on the ends of the upper side of the screen of the screen surface (hereinafter also referred to as “screen upper ends”) and the length of the optical path of rays incident on the ends of the lower side of the screen of the screen surface (hereinafter also referred to as “screen lower ends”) is increased. Consequently, when a projection distance is varied, trapezoidal distortion is significantly produced, and it is thus necessary to correct the trapezoidal distortion simultaneously when focus is adjusted.
  • the projection optical system of the invention can satisfactorily correct trapezoidal distortion produced when a projection distance is varied; the construction thereof will be specifically described with reference to FIGS. 19 to 23 .
  • FIG. 19(A) is a perspective view showing optical paths toward the screen surface SL. Broken lines represent the optical path of rays incident on the screen upper ends of the screen surface SL; dashed-dotted lines represent the optical path of rays incident on the screen lower ends of the screen surface SL.
  • the direction of a normal to the screen of the screen surface SL is referred to as a “z-direction”; the direction of a long side of the screen of the screen surface SL is referred to as an “x-direction”; and the direction of a short side of the screen of the screen surface SL is referred to as a “y-direction.”
  • the optical paths from the reflective surface SR to the projected image IM are constructed, in y-z cross section, as shown in FIG. 19(B)
  • the optical paths from the reflective surface SR to the projected image IM are constructed, in x-z cross section, as shown in FIG. 19(C) .
  • the reflective surface SR is located closest to the image in the projection optical system; it is a reflective surface that has an optical power.
  • the symbol SLx represents the long side of the screen
  • the symbol SLy represents the short side of the screen.
  • the symbol Pu represents the exit pupil of rays incident on the screen upper ends of the screen surface SL
  • the symbol Pd represents the exit pupil of rays incident on the screen lower ends of the screen surface SL.
  • a ray (corresponding to a chief ray in a typical optical system) passing through the center of an aperture is referred to as a “pupil center ray”, and then the centers of the exit pupils Pu and Pd are located on a plane (that is, the y-z plane) that includes the pupil center ray incident on the screen surface SL and that is perpendicular to the screen surface SL (in other words, the projected image IM).
  • the position of the exit pupil Pu coincides with the position at which rays that pass through the center of the aperture and that are incident on the screen upper ends of the screen surface SL intersect with the y-z plane; the position of the exit pupil Pd coincides with the position at which rays that pass through the center of the aperture and that are incident on the screen lower ends of the screen surface SL intersect with the y-z plane.
  • the difference between the distance from the position of the exit pupil Pu to the screen surface SL and the distance from the position of the exit pupil Pd to the screen surface SL is equal to a distance ⁇ from the position of the exit pupil Pu to the position of the exit pupil Pd.
  • a pupil center ray CX on the y-z plane is shown.
  • the projection distance P is the length of a straight line that falls perpendicularly on the screen surface SL from the intersection between the pupil center ray CX and the reflective surface SR. Hence, likewise, z-direction components of the projection distance P are only considered.
  • the projection magnification is assumed to be the average of a projection magnification ⁇ x in the direction (x-direction) of the long side of the screen of the display device surface and a projection magnification ⁇ y in the direction (y-direction) of the short side of the screen of the display device surface.
  • a projected image IM 2 obtained at a projection distance P 2 undergoes no trapezoidal distortion (because broken lines and dashed-dotted lines intersect on the screen surface SL), whereas a projected image IM 1 obtained at a projection distance P 1 undergoes trapezoidal distortion (because, on the screen surface SL, the width of a screen indicated by the broken lines is greater than that of a screen indicated by the dashed-dotted lines).
  • the projected image IM 2 without trapezoidal distortion is obtained as shown in FIG. 21(B)
  • the projected image IM 1 is obtained whose width becomes greater toward its upper side due to trapezoidal distortion as shown in FIG. 21(C) .
  • the trapezoidal distortion becomes larger.
  • a projection optical system When a projection optical system has a shorter projection distance P, it is necessary not only to focus on a position of the screen surface SL when focus is achieved but also to correct trapezoidal distortion corresponding to the projection distance P.
  • trapezoidal distortion In order to correct trapezoidal distortion produced when the projection distance P is varied, it is necessary to vary, when focus is achieved, the x-z components of the angles of incidence of rays with respect to the ends of the upper and lower sides of the screen of the screen surface SL. Trapezoidal distortion can be corrected either electrically or optically; when it is corrected electrically, an image on the screen is more likely to be degraded.
  • the projection optical system of the present invention employs a method of correcting trapezoidal distortion optically.
  • the direction of a normal to the screen of the screen surface is referred to as a “z-direction”
  • the direction of a long side of the screen of the screen surface is referred to as an “x-direction”
  • the x-z plane component of the angle of incidence with respect to the screen surface is referred to as an “incident angle ⁇ (°)”.
  • the incident angle ⁇ of rays whose incident angle ⁇ is larger is referred to as “ ⁇ f”
  • the incident angle ⁇ of rays whose incident angle ⁇ is smaller is referred to as “ ⁇ n”.
  • the incident angles ⁇ f and ⁇ n of rays incident on the left and right ends of the screen of the screen SL depend largely on the projection distance P, at least one of the incident angles ⁇ f and ⁇ n is varied when focus is achieved.
  • the absolute value of the projection magnification ⁇ increases with the projection distance P, as the absolute value of the projection magnification ⁇ is increased, the incident angle ⁇ of rays whose incident angle ⁇ is larger is decreased, or the incident angle ⁇ of rays whose incident angle ⁇ is smaller is increased, whereas, as the absolute value of the projection magnification ⁇ is decreased, the incident angle ⁇ of rays whose incident angle ⁇ is larger is increased, or the incident angle ⁇ of rays whose incident angle ⁇ is smaller is decreased.
  • a projection optical system that has at least one reflective surface as an optical surface having an optical power and that moves at least one optical device having an optical power to adjust focus, by varying, when focus is achieved, at least one of the incident angles ⁇ f and ⁇ n, it is possible not only to increase the size of the screen but also to decrease a projection distance and to satisfactorily correct trapezoidal distortion produced when the projection distance is varied.
  • a description will be given below of desired conditions for achieving further enhanced performance, compactness and the like in a construction in which trapezoidal distortion is optically corrected as described above and other effective constructions.
  • a projection optical system preferably satisfies conditional formula (1) below: 0.01 ⁇ (tan ⁇ f 1 ⁇ tan ⁇ f 2) ⁇ (tan ⁇ n 1 ⁇ tan ⁇ n 2) ⁇ ( ⁇ 2/ ⁇ 1) ⁇ 0.20 (1)
  • the direction of a normal to the screen of a screen surface is referred to as a “z-direction”
  • the direction of a long side of the screen of the screen surface is referred to as an “x-direction”
  • the x-z plane component of the angle of incidence with respect to the screen surface is referred to as an “incident angle ⁇ °)” and among rays that pass through the center of an aperture and that are incident on the ends of the upper and lower sides of the screen of the screen surface, the incident angle ⁇ of rays whose incident angle ⁇ is larger is referred to as “ ⁇ f” and the incident angle ⁇ of rays whose incident angle ⁇ is smaller is referred to as “ ⁇ n”,
  • Conditional formula (1) specifies a range of conditions, which is suitable for correcting trapezoidal distortion, for the amounts of variation of the incident angles ⁇ f and ⁇ n of rays, when focus is adjusted, that pass through the pupil center and are then incident on the ends of the upper and lower sides of the screen of the screen surface.
  • the lower limit of conditional formula (1) being violated, when, during focus adjustment, the projection distance varies with the projection magnification, the incident angles ⁇ f and ⁇ n of the rays that pass through the pupil center and are then incident on the ends of the upper and lower sides of the screen of the screen surface are not sufficiently varied during focus adjustment.
  • the minimum screen size (when the absolute value of a projection magnification is the lowest) and the maximum screen size (when the absolute value of the projection magnification is the highest) are limited by the optical performance of the projection optical system. That is, since the projection optical system focuses on a finite distance, a focus range that can satisfy optical performance requirements (field curvature and the like) is limited.
  • the values ⁇ 1 and ⁇ 2 described above are determined from this viewpoint.
  • conditional formula (1a) is satisfied: 0.02 ⁇ (tan ⁇ f 1 ⁇ tan ⁇ f 2) ⁇ (tan ⁇ n 1 ⁇ tan ⁇ n 2) ⁇ ( ⁇ 2/ ⁇ 1) ⁇ 0.15 (1a)
  • Conditional formula (1a) mentioned above specifies a further desired range of conditions within the range of conditions specified by conditional formula (1) described above.
  • conditional formula (1a) is satisfied, a satisfactory optical performance is maintained, and trapezoidal distortion can be more satisfactorily corrected without overcorrection and undercorrection. Thus, it is possible to obtain a further satisfactory projected image when a focus operation is performed.
  • conditional formulas (1) or (1a) as limiting conditions when a projection optical system is automatically designed can provide a projection optical system that practically satisfies conditional formulas (1) or (1a).
  • conditional formulas (1) or (1a) described above are preferably satisfied within the range of the ratio of ⁇ 1 and ⁇ 2 ( ⁇ 1/ ⁇ 2) corresponding to this screen size. From this viewpoint, conditional formulas (1) or (1a) described above are preferably satisfied within at least a range specified by the formula “1.3 ⁇ 1/ ⁇ 2 ⁇ 1.8”.
  • formula (1) is satisfied at a predetermined value of the ratio of ⁇ 1 and ⁇ 2 ( ⁇ 1/ ⁇ 2), if the ratio of ⁇ 1 and ⁇ 2 is less than the predetermined value, formula (1) is always satisfied.
  • conditional formula (2) is satisfied: 38 ⁇ f ⁇ 80 (2)
  • Conditional formula (2) specifies a range of conditions suitable for reducing a projection space sufficiently.
  • the lower limit of conditional formula (2) is violated, it is impossible to sufficiently reduce the projection space.
  • the projection distance is varied at a given projection magnification (when the size of the screen of a screen surface remains the same)
  • the upper limit of conditional formula (2) is violated, the angle of incidence of rays with respect to the screen surface is increased, and thus a smaller proportion of rays incident on the screen travels toward a viewer.
  • conditional formula (2a) is satisfied: 45 ⁇ f ⁇ 70 (2a)
  • Conditional formula (2a) mentioned above specifies a further desired range of conditions within the range of conditions specified by conditional formula (2) described above.
  • a projection space can be more reduced.
  • an appropriate number of rays that are incident on a screen surface and that then travel toward a viewer can be secured.
  • the distance from the exit pupil of rays that are incident on a screen at the incident angle ⁇ f to the screen is preferably shorter than that from the exit pupil of rays that are incident on the screen at the incident angle ⁇ n to the screen.
  • the length of the optical path of rays incident on screen upper ends (rays incident at the incident angle ⁇ f) is longer than that of the optical path of rays incident on screen lower ends (rays incident at the incident angle ⁇ n), field curvature is produced greatly.
  • the position of the exit pupil of rays incident on the screen upper ends is brought close to the screen as compared with the position of the exit pupil of rays incident on the screen lower ends, and thus the difference in the length of the optical path from the position of the exit pupil to the screen between the upper and lower portions of the screen is reduced, with the result that field curvature is easily corrected.
  • conditional formula (3) is satisfied: 1 ⁇ ( ⁇ 1+ ⁇ 2)/(2 ⁇ P 1) ⁇
  • a ray passing through the center of an aperture is referred to as a “pupil center ray”
  • the length of a normal falling perpendicularly on the screen surface from the intersection between a reflective surface that is located closest to the screen, among reflective surfaces having an optical power and the pupil center ray is assumed to be a projection distance
  • Conditional formula (3) specifies a range of conditions suitable for satisfactorily correcting trapezoidal distortion produced when the projection distance is varied in a projection optical system having a reflective surface and an extremely small projection space.
  • the lower limit of conditional formula (3) When the lower limit of conditional formula (3) is violated, the difference between the position of the exit pupil of rays incident on the screen upper ends of the screen surface and the position of the exit pupil of rays incident on the screen lower ends of the screen surface is reduced. This makes it difficult to correct field curvature.
  • the upper limit of conditional formula (3) is violated, the difference between the position of the exit pupil of rays incident on the screen upper ends of the screen surface and the position of the exit pupil of rays incident on the screen lower ends of the screen surface is increased. This makes it difficult to correct field curvature when focus is achieved.
  • conditional formula (4) 160 ⁇ ( x 1 /P 1) ⁇
  • a ray passing through the center of an aperture is referred to as a “pupil center ray” and the length of a normal falling perpendicularly on the screen surface from the intersection between a reflective surface that is located closest to the screen among reflective surfaces having an optical power and the pupil center ray is assumed to be a projection distance
  • Conditional formula (4) specifies a range of conditions suitable for reducing a projection space. When the lower limit of conditional formula (4) is violated, it is impossible to sufficiently achieve the reduction of the projection space. When the upper limit of conditional formula (4) is violated, since the angle of incidence of rays with respect to the screen surface is extremely increased, a smaller proportion of rays incident on the screen surface travels toward a viewer.
  • the exit pupil-to-exit pupil distance is preferably increased, whereas, as the projection distance P is decreased, the exit pupil-to-exit pupil distance is preferably decreased.
  • the absolute value of a projection magnification ⁇ becomes higher, and thus as the absolute value of the projection magnification ⁇ becomes higher, the exit pupil-to-exit pupil distance is preferably increased; in contrast, as the absolute value of the projection magnification ⁇ becomes lower, the exit pupil-to-exit pupil distance is preferably decreased.
  • a projection optical system that has at least one reflective surface as an optical surface having an optical power and that moves at least one optical device having an optical power to adjust focus, by moving, when focus is achieved, at least one of the exit pupil of rays incident on the screen upper ends of a screen surface and the exit pupil of rays incident on the screen lower ends of the screen surface, it is possible not only to increase the size of the screen but also to decrease a projection distance and to satisfactorily correct trapezoidal distortion produced when the projection distance is varied.
  • a projection optical system preferably satisfies conditional formula (5) below: ⁇ 0.02 ⁇ ( ⁇ 1 ⁇ 2) ⁇ 2 ⁇ / ⁇ ( ⁇ 1+ ⁇ 2) ⁇ 1 ⁇ 0.2 (5)
  • Conditional formula (5) specifies a range of conditions, which is suitable for correcting trapezoidal distortion, for the amount of variation of an exit pupil-to-exit pupil distance as the projection magnification is varied.
  • conditional formula (5) being violated, if focus is adjusted when a projection distance is increased, the exit pupil-to-exit-pupil distance of rays incident on the screen upper and lower ends of the screen surface is decreased, with the result that trapezoidal distortion becomes worse.
  • conditional formula (5a) is satisfied: 0.0001 ⁇ ( ⁇ 1 ⁇ 2) ⁇ 2 ⁇ / ⁇ ( ⁇ 1+ ⁇ 2) ⁇ 1 ⁇ 0.2 (5a)
  • Conditional formula (5a) mentioned above specifies a further desired range of conditions within the range of conditions specified by conditional formula (5) described above.
  • conditional formula (5a) is satisfied, a satisfactory optical performance is maintained, and trapezoidal distortion can be more satisfactorily corrected without overcorrection and undercorrection. Thus, it is possible to obtain a further satisfactory projected image when a focus operation is performed.
  • a projection optical system preferably includes at least one refractive optical device having an optical power.
  • a refractive optical device having an optical power it is possible to correct aberrations, such as a chromatic aberration produced by a color composition prism, that cannot be corrected by a reflective surface alone.
  • the rotationally symmetrical axes of at least two optical devices coincide.
  • a coaxial optical construction facilitates the assembly of a projection optical system.
  • a projection optical system is provided with two or more refractive optical devices whose rotationally symmetrical axes coincide, and this facilitates the assembly and production of the projection optical system, with the result that cost reduction can be achieved.
  • a projection optical system preferably moves at least one reflective surface when focus is adjusted.
  • a construction in which at least a reflective surface is moved when focus is adjusted specifically, a construction in which a reflective optical device is only moved or a construction in which a reflective optical device and a refractive optical device are moved
  • the construction in which at least a reflective surface is moved when focus is adjusted it is possible to correct distortion of an image plane that is produced on the ends of the screen of a screen surface when focus is adjusted.
  • a projection optical system preferably moves at least one refractive optical device when focus is adjusted. Since a refractive optical device can be reduced in size as compared with a reflective optical device such as a mirror, it is possible to simplify a focus mechanism with a refractive optical device. Thus, with a simplified and small-sized focus mechanism, it is possible to satisfactorily correct aberrations.
  • a total of two optical devices namely, one reflective optical device and one refractive optical device are preferably moved.
  • the length of the optical path of rays incident on a screen surface greatly differs between the screen upper portion and the screen lower portion of the screen surface, it is necessary not only to focus on the center of the screen but also to correct the inclination of an image plane with respect to the screen surface when focus is adjusted.
  • One or two reflective surfaces are preferably provided between a display device surface and a screen surface.
  • a projection optical system preferably has two or more reflective surfaces. With two or more reflective surfaces, it is possible to fold a projection optical system in a direction substantially parallel to a screen surface. This makes it possible to reduce the size of a projection optical system in the direction of the depth of the screen, and this allows the projection space of the projection optical system to be reduced.
  • By adding a reflective surface to a projection optical system to fold an optical path it is possible to reduce the size of the projection optical system in the direction of the height of the screen.
  • All reflective surfaces preferably have an optical power.
  • reflective surfaces having an optical power it is possible to correct aberrations on the reflective surfaces; this makes it possible to correct the aberration of the entire projection optical system.
  • reflective surfaces having an optical power it is possible to obtain higher optical performance.
  • a reflective surface is preferably placed closest to a screen surface within a projection optical system. By placing a reflective surface close to the screen surface to fold an optical path, it is possible to reduce a space required for projection of an image. Since light beams of different angles of view that are incident on a reflective surface are separated, as the reflective surface, a reflective surface having a free-form surface shape is arranged. Thus, it is possible to obtain a highly satisfactory aberration correction effect.
  • a reflective surface with an optical power preferably has a free-form surface shape. Since a free-form surface shape has a high degree of flexibility in design, it advantageously provides a high degree of flexibility in setting the direction in which rays are deflected. By the use of a free-form surface shape, it is possible to satisfactorily correct the inclination of an image plane and aberrations such as astigmatism. Moreover, a free-form surface that is used as a reflective surface preferably has a plane of symmetry. Advantageously, free-form surfaces having a plane of symmetry are produced and evaluated with a low degree of difficulty. Furthermore, a mirror and a refractive lens including a free-form surface are preferably formed of plastic. The use of plastic as constituent materials for optical devices (such as a mirror and a lens) including a free-form surface can reduce the cost of the optical devices.
  • a refractive surface a surface having two different optical powers in the x-axis direction and the y-axis direction (that is, an anamorphic aspherical surface) is preferably used.
  • a refractive surface having two different optical powers in the x-axis direction and the y-axis direction it is possible to correct an aberration that is asymmetrical between the x-axis direction and the y-axis direction.
  • a refractive surface having two different optical powers in the x-axis direction and the y-axis direction is preferably used as a surface that is located close to a screen surface. However, since light beams of different angles of view are separated on the surface that is located closest to the screen surface, it is preferable to arrange a reflective surface having a free-form surface shape in order to obtain a highly satisfactory aberration correction effect.
  • an intermediate image is temporarily formed within a projection optical system and is then projected by a reflective surface onto a screen surface to form an image.
  • a reflective surface By producing an aberration in an intermediate image to cancel out a distortion produced in an optical device that is located closer to a screen surface than the intermediate image, it is possible to obtain satisfactory optical performance on the screen surface even in a wide-angle projection optical system.
  • the formation of an intermediate image can reduce the size of a reflective surface, and this facilitates the assembly of the reflective surface.
  • a reflective surface that is located closest to a screen surface is preferably a concave surface.
  • a concave reflective surface as the reflective surface that is located closest to the screen surface, it is possible to form an intermediate image by the optical power of the concave reflective surface.
  • an aberration produced in the intermediate image it is possible to correct the aberration of the entire projection optical system, such as distortion and the inclination of an image plane.
  • the reflective surface that is located closest to the screen surface is a convex reflective surface, it is necessary to use not only a convex mirror but also an optical device having a positive optical power in order to form a temporarily formed intermediate image onto the screen surface. For this reason, when an intermediate image is formed, it is difficult to achieve size reduction.
  • the reflective surface that is located closest to the screen surface is a convex reflective surface and no intermediate image is formed, it is preferable to add a refractive or reflective optical device having a free-form surface shape in order to correct aberration.
  • FIGS. 1 , 4 , 7 , 10 , 13 and 16 the optical constructions (such as the optical arrangements and the projection optical paths) of the entire projection optical paths from a display device surface SG to a screen surface SL in the first to sixth embodiments are shown in cross section (in cross section on a short side), as seen in the direction of a long side of the screen of the display device surface SG.
  • FIGS. 1 , 4 , 7 , 10 , 13 and 16 show, in y-z cross section, the optical constructions of the first to sixth embodiments of the projection optical system PO.
  • the projection optical system. PO of the first to sixth embodiments is composed of: a refractive optical system LG formed with a plurality of lenses Li and the like; and a curved mirror MR or first and second curved mirrors M 1 and M 2 , which are arranged sequentially from the reduction side (the side of the display device surface SG) to the enlargement side (the side of the screen surface SL).
  • the projection optical system PO adjusts focus by moving at least one optical device having an optical power.
  • the projection optical system PO is symmetrical with respect to the y-z plane.
  • the reflective surfaces of the curved mirror MR and the first and second curved mirrors M 1 and M 2 are symmetrical with respect to a plane, and their symmetry planes are the y-z plane.
  • the optical constructions of the embodiments will be described in detail below.
  • the optical power of a free-form surface which will be described later, refers to an optical power in the vicinity of the intersection between a screen-center chief ray and the reflective surface during proximity
  • the refractive optical system LG is composed of an aperture ST and first to seventh lenses L 1 to L 7 , which are arranged sequentially from the reduction side (the side of the display device surface SG).
  • the first lens L 1 is a positive meniscus lens (both sides of which have a rotationally symmetrical aspherical surface) convex to the reduction side.
  • the second lens L 2 is a cemented lens composed of a positive biconvex lens and a negative biconcave lens.
  • the third lens L 3 is a positive biconvex lens.
  • the fourth lens L 4 is a positive biconvex lens.
  • the fifth lens L 5 is a positive biconvex lens.
  • the sixth lens L 6 is a negative meniscus lens (both sides of which have a rotationally symmetrical aspherical surface) convex to the reduction side.
  • the seventh lens L 7 is a negative biconcave lens (where the surface of the reduction side is a rotationally symmetrical aspherical surface and the surface of the enlargement side is an anamorphic aspherical surface).
  • the first and second curved mirrors M 1 and M 2 On the enlargement side (the side of the screen surface SL) of the refractive optical system LG, the first and second curved mirrors M 1 and M 2 , whose reflective surfaces are shaped in the form of a free-form surface, are arranged.
  • the first mirror M 1 has a positive optical power in the x-direction and a negative optical power (substantially no optical power) in the y-direction; the second mirror M 2 has a positive optical power.
  • the second mirror M 2 has a higher optical power in the x-direction than that in the y-direction.
  • An image on the display device surface SG is formed within the projection optical system PO.
  • the refractive optical system LG is composed of an aperture ST and first to seventh lenses L 1 to L 7 , which are arranged sequentially from the reduction side (the side of the display device surface SG).
  • the first lens L 1 is a positive meniscus lens (both sides of which have a rotationally symmetrical aspherical surface) convex to the reduction side.
  • the second lens L 2 is a cemented lens composed of a positive biconvex lens and a negative biconcave lens.
  • the third lens L 3 is a positive biconvex lens.
  • the fourth lens L 4 is a positive biconvex lens.
  • the fifth lens L 5 is a positive biconvex lens.
  • the sixth lens L 6 is a negative meniscus lens (both sides of which have a rotationally symmetrical aspherical surface) convex to the reduction side.
  • the seventh lens L 7 is a negative biconcave lens (where the surface of the reduction side is a rotationally symmetrical aspherical surface and the surface of the enlargement side is an anamorphic aspherical surface).
  • the first and second curved mirrors M 1 and M 2 On the enlargement side (the side of the screen surface SL) of the refractive optical system LG, the first and second curved mirrors M 1 and M 2 , whose reflective surfaces are shaped in the form of a free-form surface, are arranged.
  • the first mirror M 1 has a positive optical power in the x-direction and a positive optical power (substantially no optical power) in the y-direction; the second mirror M 2 has a positive optical power.
  • the second mirror M 2 has a higher optical power in the x-direction than that in the y-direction.
  • An image on the display device surface SG is formed within the projection optical system PO.
  • the refractive optical system LG is composed of first to fourth lenses L 1 to L 4 , an aperture ST and fifth to eighth lenses L 5 to L 8 , which are arranged sequentially from the reduction side (the side of the display device surface SG).
  • the first lens L 1 is a positive biconvex lens (both sides of which have a rotationally symmetrical aspherical surface).
  • the second lens L 2 is negative biconcave lens.
  • the third lens L 3 is a cemented lens composed of a positive biconvex lens and a negative meniscus lens concave to the reduction side.
  • the fourth lens L 4 is a positive meniscus lens (where the surface of the reduction side is a rotationally symmetrical aspherical surface) convex to the reduction side.
  • the fifth lens L 5 is a positive meniscus lens concave to the reduction side.
  • the sixth lens L 6 is a positive biconvex lens.
  • the seventh lens L 7 is a negative meniscus lens (both sides of which have a rotationally symmetrical aspherical surface) concave to the reduction side.
  • the eighth lens L 8 is a negative meniscus lens (both sides of which have a rotationally symmetrical aspherical surface) convex to the reduction side.
  • the curved mirror MR On the enlargement side (the side of the screen surface SL) of the refractive optical system LG, the curved mirror MR, whose reflective surface is shaped in the form of a free-form surface, is arranged.
  • the curved mirror MR has a positive optical power and has a higher optical power in the x-direction than that in the y-direction.
  • An image on the display device surface SG is formed within the projection optical system PO.
  • the refractive optical system LG is composed of an aperture ST and first to fifth lenses L 1 to L 5 , which are arranged sequentially from the reduction side (the side of the display device surface SG).
  • the first lens L 1 is a cemented lens composed of a negative meniscus lens (where the surface of the reduction side is a rotationally symmetrical aspherical surface) convex to the reduction side and a positive biconvex lens.
  • the second lens L 2 is a negative biconcave lens.
  • the third lens L 3 is a positive biconvex lens.
  • the fourth lens L 4 is a positive biconvex lens.
  • the fifth lens L 5 is a negative lens (where the surface of the reduction side is an anamorphic aspherical surface and the surface of the enlargement side is a free-form surface) concave to the reduction side.
  • the curved mirror MR On the enlargement side (the side of the screen surface SL) of the refractive optical system LG, the curved mirror MR, whose reflective surface is shaped in the form of a free-form surface, is arranged.
  • the curved mirror MR has a positive optical power and has a higher optical power in the x-direction than that in the y-direction.
  • An image on the display device surface SG is formed within the projection optical system PO.
  • the refractive optical system LG is composed of first and second lenses L 1 and L 2 , an aperture ST and third to ninth lenses L 3 to L 9 , which are arranged sequentially from the reduction side (the side of the display device surface SG).
  • the first lens L 1 is a cemented lens composed of a positive biconvex lens and a negative biconcave lens.
  • the second lens L 2 is a positive meniscus lens (both sides of which have a rotationally symmetrical aspherical surface) convex to the reduction side.
  • the third lens L 3 is a positive biconvex lens.
  • the fourth lens L 4 is a negative biconcave lens.
  • the fifth lens L 5 is a positive meniscus lens (both sides of which have a rotationally symmetrical aspherical surface) concave to the reduction side.
  • the sixth lens L 6 is a negative meniscus lens concave to the reduction side.
  • the seventh lens L 7 is a meniscus lens (where the surface of the reduction side is a rotationally symmetrical aspherical surface and the surface of the enlargement side is an anamorphic aspherical surface) concave to the reduction side.
  • the eighth lens L 8 is a free-form surface lens (where the surface of the reduction side is a free-form surface).
  • the ninth lens L 9 is a free-form surface lens (where the surface of the reduction side is a free-form surface).
  • the first and second curved mirror M 1 and M 2 On the enlargement side (the side of the screen surface SL) of the refractive optical system LG, the first and second curved mirror M 1 and M 2 , whose reflective surfaces are shaped in the form of a free-form surface, are arranged.
  • the first mirror M 1 has a negative optical power (substantially no optical power) in the x-direction and a positive optical power in the y-direction;
  • the second mirror M 2 has a negative optical power.
  • the second mirror M 2 has a higher negative optical power in the x-direction than that in the y-direction.
  • the refractive optical system LG is composed of first to third lenses L 1 to L 3 , an aperture ST and fourth to ninth lenses L 4 to L 9 , which are arranged sequentially from the reduction side (the side of the display device surface SG); a cover glass CG is arranged on the reduction side of the refractive optical system LG.
  • the first lens L 1 is a plano-concave lens (where the surface of the reduction side is a rotationally symmetrical aspherical surface) concave to the reduction side.
  • the second lens L 2 is a cemented lens composed of a negative biconcave lens and a positive biconvex lens.
  • the third lens L 3 is a positive meniscus lens concave to the reduction side.
  • the fourth lens L 4 is a positive biconvex lens.
  • the fifth lens L 5 is a negative biconcave lens (where the surface of the reduction side is a rotationally symmetrical aspherical surface).
  • the sixth lens L 6 is a negative meniscus lens convex to the reduction side.
  • the seventh lens L 7 is a positive meniscus lens (where the surface of the reduction side is a free-form surface) concave to the reduction side.
  • the eighth lens L 8 is a free-form surface lens (where the surface of the enlargement side is a free-form surface).
  • the ninth lens L 9 is a free-form surface lens (where the surface of the reduction side is a free-form surface).
  • the first and second curved mirror M 1 and M 2 On the enlargement side (the side of the screen surface SL) of the refractive optical system LG, the first and second curved mirror M 1 and M 2 , whose reflective surfaces are shaped in the form of a free-form surface, are arranged.
  • the first curved mirror M 1 has a positive optical power in the x-direction and a negative optical power in the y-direction;
  • the second curved mirror M 2 has a negative optical power in the x-direction and a positive optical power (substantially no optical power) in the y-direction.
  • the first to sixth embodiments by varying, when focus is achieved, at least one of the incident angles ⁇ f and ⁇ n, it is possible not only to increase the size of the screen but also to decrease the projection distance and to satisfactorily correct trapezoidal distortion produced when the projection distance is varied.
  • a total of two optical devices namely one curved mirror MR and one refractive lens, it is possible to share functions for achieving focus and correcting the inclination of an image plane, between the two optical devices. This makes it possible to obtain satisfactory performance before and after focus is achieved.
  • the first to sixth embodiments are directed to the projection optical system PO for an image projection device that enlarges and projects a display image onto the screen surface SL.
  • the display device surface SG corresponds to an image formation surface where a two-dimensional image is formed such as by modulating light intensity;
  • the screen surface SL corresponds to its projection image plane.
  • a digital micromirror device is assumed to be used as the display device, the display device is not limited to such a digital micromirror device, and any other non-light-emitting/reflective (or transmissive) display device (for example, a liquid crystal display device) suitable for the projection optical system PO of the individual embodiments may be used.
  • a digital micromirror device being used as the display device
  • light that is reflected by the micromirrors in the on state only enters the projection optical system PO and is then projected onto the screen surface SL.
  • the embodiments described above and Examples described later include the constructions of the following projection optical systems and image projection devices.
  • T1 A projection optical system that enlarges and projects an image on a display device surface onto a screen surface, including one or more reflective surfaces having an optical power between the display device surface and the screen surface, characterized in that, by moving at least one optical device having an optical power, focus is adjusted, and at least one of the incident angle of rays incident on the ends of the upper side of the screen of the screen surface and the incident angle of rays incident on the ends of the lower side of the screen of the screen surface is varied when focus is achieved.
  • T2 The projection optical system described in item (T1) above, characterized in that, when focus is adjusted by increasing a projection distance, the incident angle ⁇ of rays whose incident angle ⁇ is larger is decreased.
  • T3 The projection optical system described in item (T1) or (T2) above, characterized in that, when focus is adjusted by increasing the projection distance, the incident angle ⁇ of rays whose incident angle ⁇ is smaller is increased.
  • T4 The projection optical system described in any one of items (T1) to (T3) above, characterized in that at least one of conditional formulas (1), (1a), (2), (2a), (3), (4), (5) and (5a) described previously is satisfied.
  • T5 The projection optical system described in any one of items (T1) to (T4) above, characterized in that it includes at least one refractive optical device having an optical power.
  • T7 The projection optical system described in any one of items (T1) to (T6) above, characterized in that, in the focus adjustment, at least one reflective surface or at least one refractive optical device is moved.
  • T8 The projection optical system described in any one of items (T1) to (T7) above, characterized in that it further includes, between the display device surface and the screen surface, a flat mirror for folding an optical path.
  • T9 The projection optical system described in any one of items (T1) to (T8) above, characterized in that it includes at least one refractive surface formed with a free-form surface.
  • T10 The projection optical system described in any one of items (T1) to (T9) above, characterized in that it includes at least one reflective surface formed with a free-form surface.
  • An image projection device including a display device for forming a two-dimensional image and a projection optical system for enlarging and projecting an image on a display device surface thereof onto a screen surface, characterized in that the projection optical system includes one or more reflective surfaces having an optical power between the display device surface and the screen surface, by moving at least one optical device having an optical power, focus is adjusted and at least one of the incident angle of rays incident on the ends of the upper side of the screen of the screen surface and the incident angle of rays incident on the ends of the lower side of the screen of the screen surface is varied when focus is achieved.
  • Examples 1 to 6 that will be described below are numerical examples corresponding to the first to sixth embodiments, respectively, described above.
  • Ray diagrams ( FIGS. 1 , 4 , 7 , 10 , 13 and 16 ) showing the optical constructions of the first to sixth embodiments show the corresponding optical arrangements, projection optical paths and the like of Examples 1 to 6, respectively.
  • Tables 1 to 34 show the construction data of Examples 1 to 6;
  • Table 35 shows projection magnifications ( ⁇ x: the projection magnification in the direction of a long side of a screen, ⁇ y: the projection magnification in the direction of a short side of the screen) and the radius of the aperture R (mm) in the Examples;
  • Table 36 shows data and the like corresponding to the conditional formulas in the Examples.
  • the data shown in Table 36 is based on the projection magnifications in (A): a shortest-distance projection state and in (B): a long-distance projection state, which are shown in Table 35, in the Examples.
  • the screen sizes of screen surfaces at ⁇ 1 and ⁇ 2 are calculated from the size of the display device surface (8.294 ⁇ 11.06 mm 2 ) and the magnifications ⁇ 1 and ⁇ 2 (the screen sizes are in units of inches).
  • the symbol S0 represents the image display surface of the display device and corresponds to an object plane
  • Focus data shown in Tables 3, 9, 15, 20, 26 and 32 refers to the axial surface-to-surface distances di or the surface-vertex coordinates (XDE, YDE, ZDE), which are varied by the focusing in the Examples, and shows focus positions in (A): the shortest-distance projection state and in (B): the long-distance projection state. No data is listed that is not varied by the focusing.
  • the symbols #A are placed in the “surface Si” column for identification.
  • the surface Si that has a rotationally symmetrical aspherical surface is defined by formula (AS) below using a local orthogonal coordinate system (x, y, z) having its origin at the vertex of the surface.
  • AS formula
  • Tables 4, 10, 16, 21, 27 and 33 show data on the aspherical surfaces of the Examples.
  • the coefficient of any term that does not appear in the Tables is 0, and “E ⁇ n” stands for “ ⁇ 10 ⁇ n ” for all the data.
  • the symbols #B are placed in the “surface Si” column for identification.
  • the surfaces Si that has an anamorphic aspherical surface is defined by formula (BS) below using a local orthogonal coordinate system (x, y, z) having its origin at the vertex of the surface.
  • Tables 5, 11, 22 and 28 show data on the anamorphic aspherical surfaces of Examples 1, 2, 4 and 5.
  • the coefficient of any term that does not appear in the Tables is 0, and “E ⁇ n” stands for “ ⁇ 10 ⁇ n ” for all the data.
  • the symbols #C are placed in the “surface Si” column for identification.
  • the surface Si that has a free-form surface is defined by formula (CS) below using a local orthogonal coordinate system (x, y, z) having its origin at the vertex of the surface.
  • Tables 6, 12, 17, 23, 29 and 34 show data on the polynomial free-form surfaces of the Examples.
  • the coefficient of any term that does not appear in the Tables is 0, and “E ⁇ n” stands for “ ⁇ 10 ⁇ n ” for all the data.
  • z ( c ⁇ h 2 )/[1+ ⁇ 1 ⁇ (1 +K ) ⁇ c 2 ⁇ h 2 ⁇ ]+ ⁇ C ( j,k ) ⁇ x j ⁇ y k ⁇ (CS)
  • FIGS. 2(A) , 3 (A), 5 (A), 6 (A), 8 (A), 9 (A), 11 (A), 12 (A), 14 (A), 15 (A), 17 (A) and 18 (A) show the optical performance in the shortest-distance projection state when focus is achieved, and FIGS.
  • the spot diagrams show imaging characteristics (mm) on the screen surface SL for each of the following three lines: the C-line (with a wavelength of 656.3 nm), the d-line (with a wavelength of 587.6 nm) and the g-line (with a wavelength of 435.8 nm).
  • the field position of each spot represents coordinates (x, y) on the display device surface SG (the object plane S0).
  • the distortion diagrams show ray positions (mm) on the screen surface SL corresponding to a rectangular grid (the x-axis direction: the direction of the long side of the screen, the y-axis direction: the direction of the short side of the screen) on the display device surface SG with solid lines representing the distorted grids in the Examples and broken lines representing the grids (without distortion) of ideal image points with consideration given to the anamorphic ratio.

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